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lecture 5 - CS 188 Artificial Intelligence Spring 2010...

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1 CS 188: Artificial Intelligence Spring 2010 Lecture 5: CSPs II 2/2/2010 Pieter Abbeel – UC Berkeley Many slides from Dan Klein 1 Announcements square4 Project 1 due Thursday square4 Lecture videos reminder: don’t count on it square4 Midterm square4 Section: CSPs square4 Tue 3-4pm, 285 Cory square4 Tue 4-5pm, 285 Cory square4 Wed 11-noon, 285 Cory square4 Wed noon-1pm, 285 Cory 2
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2 Today square4 CSPs square4 Efficient Solution of CSPs square4 Search square4 Constraint propagation square4 Local Search 3 Example: Map-Coloring square4 Variables: square4 Domain: square4 Constraints: adjacent regions must have different colors square4 Solutions are assignments satisfying all constraints, e.g.: 5
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3 Constraint Graphs square4 Binary CSP: each constraint relates (at most) two variables square4 Binary constraint graph: nodes are variables, arcs show constraints square4 General-purpose CSP algorithms use the graph structure to speed up search. E.g., Tasmania is an independent subproblem! 6 Example: Cryptarithmetic square4 Variables (circles): square4 Domains: square4 Constraints (boxes): 7
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4 Example: Sudoku square4 Variables: square4 Each (open) square square4 Domains: square4 {1,2,…,9} square4 Constraints: 9-way alldiff for each row 9-way alldiff for each column 9-way alldiff for each region Example: The Waltz Algorithm square4 The Waltz algorithm is for interpreting line drawings of solid polyhedra square4 An early example of a computation posed as a CSP square4 Look at all intersections square4 Adjacent intersections impose constraints on each other ? 10
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5 Varieties of CSPs square4 Discrete Variables square4 Finite domains square4 Size d means O( d n ) complete assignments square4 E.g., Boolean CSPs, including Boolean satisfiability (NP-complete) square4 Infinite domains (integers, strings, etc.) square4 E.g., job scheduling, variables are start/end times for each job square4 Linear constraints solvable, nonlinear undecidable square4 Continuous variables square4 E.g., start-end state of a robot square4 Linear constraints solvable in polynomial time by LP methods (see cs170 for a bit of this theory) 14 Varieties of Constraints square4 Varieties of Constraints square4 Unary constraints involve a single variable (equiv. to shrinking domains): square4 Binary constraints involve pairs of variables: square4 Higher-order constraints involve 3 or more variables: e.g., cryptarithmetic column constraints square4 Preferences (soft constraints): square4 E.g., red is better than green square4 Often representable by a cost for each variable assignment square4 Gives constrained optimization problems square4 (We’ll ignore these until we get to Bayes’ nets) 15
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6 Real-World CSPs square4 Assignment problems: e.g., who teaches what class square4 Timetabling problems: e.g., which class is offered when and where?
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